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A New Large Nc Relation As a Probe of Skyrmions and Their Holographic

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A New Large Nc Relation As a Probe of Skyrmions and Their Holographic Tests of Universality of Baryon Form Factors In Holographic QCD A. Cherman, T.D. Cohen, M. Nielsen, PRL103(09) Univ. of Maryland and Univ. of Sao Paulo Low x Meeting, September 2009 QCD: strong-coupled theory AdS/QCD models: successful at reproducing low energy hadronic observables • two classes of AdS/QCD models Top-down models: Botton-up models: arise from sting theory QCD large Nc dual to a classical 5D theory D4/D8 system gauge theory confining as QCD field content 5D matched AdS/CFT requires large Nc to low energy chiral and ´t Hooft coupling symmetry of QCD Both cases: large Nc is required QCD is a weakly-interacting theory of long -lived mesons in the • ‘t Hooft, 1973 large Nc limit. • In the large Nc limit, baryons are ‘soliton -like’ configurations of meson fields. Witten, 1979 1 • Baryon masses scale as Nc (composed of Nc quarks), 1/2 interactions with mesons scale as Nc . • Unlike mesons, baryons are not narrow at large Nc. • Nucleons, deltas, become degenerate. Mass splitting -1 scales as Nc . • In contrast to the pure meson sector, meson loops make leading order contributions to baryon properties at large Nc. • Variety of baryon models (Skyrme models) use large Nc properties of baryons for inspiration. Skyrme, 1961 • Baryons modeled as quantum states of slowly rotating Adkins, Nappi, hedgehog Skyrmions of meson fields. Witten, 1983 Dashen, Manohar, Jenkins,1993-95 Model-independent relations for baryons valid at large Nc • Goldberger-Treiman relation: • Relation is model-indepedent, and follows from chiral symmetry. • Nucleon and delta couplings with pions are related by • • This relation follows just from the large Nc limit • New model-independent relation: • Ratio of nucleon form factors in position space, evaluated at large distances: • Relation depends on both the large Nc and chiral limits. • Can serve as a useful and highly non -trivial probe of large Nc baryon models. Model independence of the ratio Leading large r behavior of form factors in large Nc ChiPT are mediated by pions Three pion interaction - comes from anomaly. Two pion interaction. • In the large Nc limit, leading contributions to isovector electric and isoscalar magnetic form factors are sensitive to the nucleon - delta mass splitting ~ 1/N c (Cohen PLB 359) ratio is independent of Skyrme-type models SU(2) matrix • Original Skyrme model includes only pion fields. • Baryons appear as quantum states of slowly rotating hedgehog Skyrmions of pion fields. hedgehog ansatz: in the large r limite f(r) goes like in the Skyrme model: 5D Skyrmions Pomarol-Wulzer holographic baryon model Pomarol, Wulzer, NPB809:347 -361,2009. Panico, Wulzer, arXiv:0811.2211 • Bottom-up AdS /QCD model: uses hard -wall AdS background, with two U(2) 5D gauge fields, L M RM, associated with 4D left and right quark currents ( AdS /CFT dictionary). • Chiral symmetry broken by choice of IR boundary conditions for 5D gauge fields. • Has a 5D CS term to get anomaly physics right. • this model looks quite different from 4D Skyrme models: there are no explicit pion fields. • Baryons appear as quantum states of slowly rotating Skyrmion-like hedgehog configurations of the 5D gauge field. • Skyrmions are stabilized by the CS term. gA = 0.65 in the original Skyrme model in the large r limit large Nc and chiral physics handled correctly in Pomarol-Wulzer model Baryons as Holographic Instantons Sakai-Sugimoto model Hata et al, hep -th/0701280 Hashimoto, Sakai, Sugimoto, PTP120:1093-1137,2008 • Top-down AdS/QCD model: baryons are described as instantons in a 5D Yang-Mills and CS theory, formulated in the D4/D8 model. • AM :5D U( Nf) field, FMN : field strength, CS 5 -form • Model expected to make sense when Nc and the ‘t Hooft coupling are large. • CS term stabilizes the instanton size to be of order • At large higher derivative terms are not suppressed, and 1/ expansion is not well justified SS in the large r limit related with meson rho mass • Model does not satisfy large Nc relation. • Ratio depends on model parameters. • Model fails because it does not treat chiral symmetry correctly. • Another signal: the isovector charge radius is finite in the model. It is known to be infinite in chiral perturbation theory in the chiral limit. • These results suggest that the Sakai -Sugimoto instanton model fails to correctly describe the long-range part of large Nc baryon physics. Summary • We discussed a model -independent large Nc relation for baryons. • Relation probes consistency of implementation of chiral and large Nc physics in baryon models. • In this case, the probe reveals that some holographic models get large Nc chiral physics right, while others do not. • This situation illustrates the utility of large Nc analysis as a diagnostic tool for probing models. • Relation should be checked in other new large Nc baryon models. http://www.sbf1.sbfisica.org.br/eventos/extras/hadrons2010/ XI HADRON PHYSICS March, 22 - 27, 2010, São Sebastião, Brazil origem of problem: large expansion. • SS model: pion nucleon coupling scales as • pion loops contributions to nucleon properties are discarded if the large limit is taken prior to the large Nc limit. • It is necessary to go beyond large limit in the SS model to capture large Nc chiral physics. Definitions These position-space form factors can be related to the standard (experimentally accessible) momentum -space form factors by the appropriate Fourier transforms..
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